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arXiv · 2601.04014

On a conjecture of Andrews and Bachraoui

Koustav Banerjee·Kathrin Bringmann·William J. Keith
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Abstract

Recently, Andrews and Bachraoui considered a generating function $F_{k,m}(q)$ associated with certain two-color partitions, and conjectured that this function has non-negative coefficients for $m=1$. They showed this property for $1 \leq k \leq 4$. In this note, we prove that $F_{k,1}(q)$ has non-negative coefficients for $5 \leq k \leq 10$. Moreover, we show that, as $k\to\infty$, $F_{k,1}(q)$ is related to Ramanujan's third order mock theta function $\omega(q)$ and to quotients of certain $q$-binomial coefficients.

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Koustav Banerjee, Kathrin Bringmann, William J. Keith. 2026-01-07. On a conjecture of Andrews and Bachraoui. https://arxiv.org/abs/2601.04014

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